The results of an experimental study of the energy spectrum of the valence band in a HgTe quantum well of width d < 6.3 nm with normal spectrum in the presence of a strong spin-orbit splitting are reported. The analysis of the temperature, magnetic field and gate voltage dependences of the Shubnikov-de Haas oscillations allows us to restore the energy spectrum of the two valence band branches, which are split by the spin-orbit interaction. The comparison with the theoretical calculation shows that a six-band kP theory well describes all the experimental data in the vicinity of the top of the valence band.

We investigate experimentally transport in gated microsctructures containing a band-inverted HgTe/Hg0.3Cd0.7Te quantum well. Measurements of nonlocal resistances using many contacts prove that in the depletion regime the current is carried by the edge channels, as expected for a twodimensional topological insulator. However, high and non-quantized values of channel resistances show that the topological protection length (i.e. the distance on which the carriers in helical edge channels propagate without backscattering) is much shorter than the channel length, which is ∼ 100 µm. The weak temperature dependence of the resistance and the presence of temperature dependent reproducible quasi-periodic resistance fluctuations can be qualitatively explained by the presence of charge puddles in the well, to which the electrons from the edge channels are tunnel-coupled.

The results of an experimental study of the magnetoresistivity and the Hall and Shubnikov-de Haas effects for a heterostructure with a HgTe quantum well of 20.2 nm width are reported. The measurements were performed on gated samples over a wide range of electron and hole densities including the vicinity of a charge neutrality point. Analyzing the data, we conclude that the electron and hole energy spectra are in qualitative agreement with those calculated within the framework of kP model. The electron and hole subbands are overlapped due to the nonmonotonic dispersion of the hole subband resulting in a semimetallic state. The main result of the paper, however, is the drastic quantitative difference in the experimental and calculated spectra of the hole subband. So, the hole effective mass found from the analysis of the Shubnikov-de Haas oscillations is positive and equal to approximately 0.2m 0 and practically independent of the quasimomentum (k) starting from k 2 0.7 × 10 12 cm −2 , while the theory predicts negative (electronlike) effective mass up to k 2 6 × 10 12 cm −2 . The experimental effective mass near k = 0, where the hole energy spectrum is electronlike, is close to −0.005m 0 , whereas the theoretical value is about −0.1m 0 .

Energy spectra both of the conduction and valence bands of the HgTe quantum wells with a width close to the Dirac point were studied experimentally. Simultaneous analysis of the Shubnikov-de Haas oscillations and Hall effect over a wide range of electron and hole densities gives surprising result: the top of the valence band is strongly split by spin-orbit interaction while the splitting of the conduction band is absent, within experimental accuracy. Astonishingly, but such a ratio of the splitting values is observed as for structures with normal spectrum so for structures with inverted one. These results do not consistent with the results of kP calculations, in which the smooth electric filed across the quantum well is only reckoned in. It is shown that taking into account the asymmetry of the quantum well interfaces within a tight-binding method gives reasonable agreement with the experimental data.